Well that sucks for the dog certainly... but i have personally seen a few dog in my area kill deer. I live on a farm and almost everyone has protecting dogs. I watched a great pyrnese and also a great dane kill a deer. Yes the dogs were roughly 140lbs or more at the time so it was about the same size as the doe in the footage. And all these wolves run in pack comments are dumb... 1 wolf is deadly enough. One wolf is usually used to distract its prey while the others attack... its just purely outsmarting the opponent. Deer are relatively one tracked when they feel threatened its attention never strayed away at that dog and someone could have ran towards it to scare it or even attempt to tackle it.
I would like you to test that theory out and videotape it so we can view the lolz of you getting your head stomped in by a deer.